1. Field of the Invention
The present invention relates to a secret sharing apparatus and a secret sharing method capable of performing a restoration process with a small amount of data.
2. Description of the Related Art
In the related art, a technique which uses polynomial interpolation has been proposed as a threshold secret sharing scheme (for example, refer to A. Shamir, “How to Share a Secret”, Communications of the ACM, November 1979, Volume 22, No. 11). However, this technique takes time for a calculation process, and is thus unsuitable for a case where real-time performance is demanded or a case where the technique is used for a large amount of data.
As ways for solving the above problem, a threshold secret sharing scheme which uses an XOR operation has been proposed (for example, refer to JP-A-2007-124032, JP-A-2008-145917 and JP-A-2008-203720).
However, in these threshold secret sharing schemes using the XOR operation, if a random number sequence is leaked, there is a risk that original data is easily inferred from shared data. Further, since the data amount of shared data has the same size as in the original data, if the number of shares is increased, a large capacity of memory is necessary. In addition, a certain limit such as limit in the number of threshold values may be present as a threshold secret sharing scheme.
An object of some aspects of the invention is to provide a technique which realizes a secure threshold secret sharing scheme using an XOR operation to prevent original data from being inferred from shared data. Further, it provides a secret sharing apparatus, a sharing apparatus and a secret sharing method capable of reducing the data amount of shared data and freely setting the number of shares and a threshold value to provide easy usage.